Abstract : A phenomenological characterization of hysteresis in magnetostrictive materials is presented. Such hysteresis is due to both the driving magnetic fields and stress relations within the material and is significant throughout most of the drive range of magnetostrictive transducers. An accurate characterization of the hysteresis and material nonlinearities is necessary to fully utilize the actuator/sensor capabilities of the magnetostrictive materials. Such a characterization is made here in the context of generalized Preisach operators. This yields a framework amenable to proving the well-posedness of structural models that incorporate the magnetostrictive transducers. It also provides a natural setting in which to develop practical approximation techniques. An example illustrating this framework in the context of a Timoshenko beam model is presented.